Kernel quadrature with DPPs
Machine Learning
2020-01-03 v3 Machine Learning
Abstract
We study quadrature rules for functions from an RKHS, using nodes sampled from a determinantal point process (DPP). DPPs are parametrized by a kernel, and we use a truncated and saturated version of the RKHS kernel. This link between the two kernels, along with DPP machinery, leads to relatively tight bounds on the quadrature error, that depends on the spectrum of the RKHS kernel. Finally, we experimentally compare DPPs to existing kernel-based quadratures such as herding, Bayesian quadrature, or leverage score sampling. Numerical results confirm the interest of DPPs, and even suggest faster rates than our bounds in particular cases.
Keywords
Cite
@article{arxiv.1906.07832,
title = {Kernel quadrature with DPPs},
author = {Ayoub Belhadji and Rémi Bardenet and Pierre Chainais},
journal= {arXiv preprint arXiv:1906.07832},
year = {2020}
}